/*---------------------------------------------------------------------------*\
  =========                 |
  \\      /  F ield         | foam-extend: Open Source CFD
   \\    /   O peration     | Version:     4.1
    \\  /    A nd           | Web:         http://www.foam-extend.org
     \\/     M anipulation  | For copyright notice see file Copyright
-------------------------------------------------------------------------------
License
	This file is part of foam-extend.

	foam-extend is free software: you can redistribute it and/or modify it
	under the terms of the GNU General Public License as published by the
	Free Software Foundation, either version 3 of the License, or (at your
	option) any later version.

	foam-extend is distributed in the hope that it will be useful, but
	WITHOUT ANY WARRANTY; without even the implied warranty of
	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
	General Public License for more details.

	You should have received a copy of the GNU General Public License
	along with foam-extend.  If not, see <http://www.gnu.org/licenses/>.

Class
	Foam::Polynomial

Description
	Polynomial templated on size (order):

	\verbatim
		poly = sum(coeffs[i]*x^i) + logCoeff*log(x)
	\endverbatim

	where <tt> 0 <= i <= N </tt>

	- integer powers, starting at zero
	- \c value(x) to evaluate the poly for a given value
	- \c derivative(x) returns derivative at value
	- \c integral(x1, x2) returns integral between two scalar values
	- \c integral() to return a new, integral coeff polynomial
	  - increases the size (order)
	- \c integralMinus1() to return a new, integral coeff polynomial where
	  the base poly starts at order -1

SourceFiles
	Polynomial.C

\*---------------------------------------------------------------------------*/

#ifndef Polynomial_H
#define Polynomial_H

#include "word.H"
#include "scalar.H"
#include "Ostream.H"
#include "VectorSpace.H"
#include "StaticAssert.H"

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

namespace Foam
{

// Forward declaration of classes
template<int PolySize>
class Polynomial;

// Forward declaration of friend functions
template<int PolySize>
Ostream& operator<<
(
	Ostream&,
	const Polynomial<PolySize>&
);



template<int PolySize>
class Polynomial
:
	public VectorSpace<Polynomial<PolySize>, scalar, PolySize>
{
	//- Size must be positive (non-zero)
	StaticAssert(PolySize > 0);

	// Private data

		//- Include the log term? - only activated using integralMinus1()
		bool logActive_;

		//- Log coefficient - only activated using integralMinus1()
		scalar logCoeff_;


public:

	typedef Polynomial<PolySize> polyType;

	typedef Polynomial<PolySize+1> intPolyType;


	// Constructors

		//- Construct null, with all coefficients = 0.0
		Polynomial();

		//- Copy constructor
		Polynomial(const Polynomial&);

		//- Construct from C-array of coefficients
		explicit Polynomial(const scalar coeffs[PolySize]);

		//- Construct from a list of coefficients
		explicit Polynomial(const UList<scalar>& coeffs);

		//- Construct from Istream
		Polynomial(Istream&);

		//- Construct from name and Istream
		Polynomial(const word& name, Istream&);


	// Member Functions

		// Access

			//- Return true if the log term is active
			bool logActive() const;

			//- Return the log coefficient
			scalar logCoeff() const;


		// Evaluation

			//- Return polynomial value
			scalar value(const scalar x) const;

			//- Return derivative of the polynomial at the given x
			scalar derivative(const scalar x) const;

			//- Return integral between two values
			scalar integral(const scalar x1, const scalar x2) const;

			//- Return integral coefficients.
			//  Argument becomes zero'th element (constant of integration)
			intPolyType integral(const scalar intConstant = 0.0) const;

			//- Return integral coefficients when lowest order is -1.
			//  Argument becomes zero'th element (constant of integration)
			polyType integralMinus1(const scalar intConstant = 0.0) const;


	//- Ostream Operator
	friend Ostream& operator<< <PolySize>
	(
		Ostream&,
		const Polynomial&
	);
};


// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

} // End namespace Foam

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

#ifdef NoRepository
	#include "Polynomial.C"
	#include "PolynomialIO.C"
#endif

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

#endif

// ************************************************************************* //
